I have reviewed some awesome comics on this blog over the past few months. Two of them have had LGBT characters (i.e. Young Avengers and Batwoman). Representation is important. You want to read about characters that you have something in common with and that connection makes them memorable.
I found this video today with two people who have way more knowledge on LGBT characters in comics than I do. Their enthusiasm and hope for the future of mainstream comics is so awesome to see. I learned a lot from watching this video and I hope you will too.
Unfortunately, this video only focuses on superhero comics. It also does not give many suggestions for comics outside what the two hosts discuss. Despite these two points, I think the video is important because it communicates a lot about the changes that mainstream comics are going through and the difficulties they are facing. They don't cover everything but this video is still a great introduction to the topic.